An automatic steering system for a work vehicle (10) comprises a position sensor (38) for detecting a position of the vehicle (10), a memory (44) for storing information about a nominal path of the vehicle (10) and a control unit (40) coupled to the position sensor (38), to the memory (44) and to a steering actuator (42) for steering the vehicle (10). The control (40) submits control signals to the steering actuator (42) that depend upon a feedback gain and a lateral offset between the actual position and the nominal path. The feedback gain depends upon a sensed payload of the vehicle.